1. Field of the Invention
The present invention relates generally to flow control devices for hydraulic pumps and, more particularly, to enhancing the stability of flow control devices used in controlling the output of hydraulic pumps in power steering systems.
2. Description of the Prior Art
It is known in power steering circuits to control the output of the hydraulic pump with a flow control sub-assembly. Sub-assemblies and pumps of this type are produced by Saginaw Division of General Motors of Saginaw, Mich.; Ford Motor Co. of Dearborn, Mich.; and Honda Motor Co. of Japan. In the flow control sub-assembly, hydraulic flow is controlled by a piston which moves reciprocally in a flow control output cylinder to open and close a bypass hole. Hydraulic flow is delivered from the pump to an output chamber formed between a high pressure end of the piston in the flow control output cylinder and a pump output fitting. Fluid from the output chamber passes through a venturi in the flow control output fitting and on to the power steering system. The flow passing through the venturi is at a reduced pressure from the pressure in the output chamber. A pressure sensing orifice in the output fitting measures the reduced pressure in the venturi and delivers the pressure through passages in the housing to a low pressure chamber formed in the bore at an opposite end of the piston. A compression spring in the low pressure chamber biases the piston towards the output fitting to close the bypass hole. The combined force of the compression spring and the reduced pressure from the pressure sensing orifice oppose the pressure of the pump output acting on the high pressure end of the piston.
In addition, a pressure relief for fluid in the low pressure chamber is provided by a bypass device located in the piston. This function is activated whenever fluid pressure demand by the steering system exceeds a preselected bypass pressure value such as by a driver forcing the dirigible wheels against a curb. The bypass device's function is to pass fluid at any pressure value exceeding the preselected bypass pressure value directly into the bypass hole. The pressure sensing orifice then impedes the flow of fluid toward the low pressure chamber and its pressure value drops to the preselected bypass pressure value. This reduction of pressure enables the piston to compress the spring and move to a position whereat it partially uncovers the bypass hole and allows excess fluid to flow back to the pump via the bypass hole.
If flow issuing from the output flow nozzle is too great, then the force derived from the measured pressure differential between the pump output and the reduced pressure in the venturi will exceed the force provided by the compression spring and the flow control piston will move away from the end of the output fitting. The piston, then, partially uncovers the bypass hole to pass excess pumped fluid back toward an input port of the power steering pump and its reservoir. When a nominal design flow value is obtained, the piston is maintained in a first flow regulating position. Should pressure demand increase in the system and the uncovered portion of the bypass hole conduct an excessive amount of pumped fluid to the reservoir, then the measured pressure differential between the output pump pressure and reduced venturi pressure decreases. The spring forces the piston back toward the end of the output fitting to a new flow regulating position to re-establish the design flow. Thus, the piston moves toward and away from the output fitting in response to changes in the system pressure demand.
The mass of the piston and hydraulic inductance of the passages in the housing comprise mass or mass-like elements, which are supported by the spring in a spring-mass system. The passages and the low pressure chamber form a substantially deadheaded hydraulic subsystem fed by the pressure sensing orifice in a series arrangement. Fluid flow through the pressure sensing orifice is related to pressure drop therethrough in a square law manner. As will be shown below, resistance to flow therethrough is proportional to either the square root of pressure drop, or alternately, fluid flow rate therethrough. However, since the pressure sensing orifice is feeding a substantially deadheaded hydraulic sub-system with concomitant nominally zero values of pressure drop and fluid flow rate therethrough, flow resistance has a value which is substantially zero. Thus, the sub-system forms a resonant hydro-mechanical sub-system which can be easily excited by bypass flow non-linearities to produce an unwanted oscillation of the piston. The oscillation may result in flow and/or pressure variations in the hydraulic flow delivered by the flow control sub-assembly to the power steering system. This is a servo system wherein these variations may combine with structural resonances present in the steering system and/or vehicle structure to produce a significant vibration known as "shudder" which can be felt by the driver. Stability problems associated with servo systems are discussed in DiStefano, Stubberud, and Williams in Schaum's Outline of Theory and Problems of Feedback and Control Systems, (McGraw-Hill Book Company, N.Y.).
Typically an engine operating at low speeds (especially when the engine is operated in a loaded condition such as being in gear with the air conditioner on) has significant variations in its speed. Since the pump is driven by the engine, it has substantially identical variations in both its speed and output flow rate. These output flow rate variations can easily excite the above described piston oscillations. These oscillations, in turn, can cause even more significant flow variations to the power steering system as mentioned above and described in detail below. The primary cause of the variation of engine rotational speed is the individual power pulses determined by the firing frequency of the engine's cylinders. A six cylinder engine has three power strokes per revolution and when operated at idle speed may have a firing frequency of about 36 Hz, and an associated rotational velocity ripple of approximately 10% from peak to peak. In addition, many engines also have a rotational velocity ripple at the fundamental frequency (or about 12 Hz for a six cylinder engine) with a concomitant rotational velocity ripple of perhaps 5% peak-to-peak. Because the pump is directly driven by the engine, these rotational velocity ripple characteristics concomitantly cause similar flow rate ripple in the output flow from the pump. Such low speed flow rate ripple can be coupled with systemic flow non-linearities described below to excite oscillation at frequencies near the resonant frequency of the above described spring-mass sub-system. This oscillation further exaggerates the flow variations.
The mechanism producing the oscillation can be demonstrated mathematically by the equations set forth below. The combination of the flow-pressure relationship for the pressure sensing orifice is defined by the equation ##EQU1## and its flow resistance is defined by the equation ##EQU2## where Q.sub.pso is flow rate therethrough, A.sub.pso is effective area of the pressure sensing orifice, .rho. is fluid density, P.sub.pso is pressure drop therethrough and R.sub.pso is flow resistance therethrough. Since P.sub.pso and Q.sub.pso substantially have zero values in the deadheaded condition, R.sub.pso has a zero value also.
The resonant frequency of the system can be determined as follows. The spring constant can be transformed into an equivalent hydraulic capacitance by dividing its value into the square of the flow control piston area. The mass of the flow control piston can be transformed into an equivalent hydraulic inductance by dividing its value by the square of the flow control piston area. The values and their dimensions are ##EQU3## where C.sub.h is the equivalent hydraulic capacitance of the spring constant, A.sub.p is the flow control piston area, K.sub.s is the spring constant, L.sub.p is the equivalent hydraulic inductance of the flow control piston mass and M.sub.p is the flow control piston mass. The total effective hydraulic inductance L.sub.t is obtained by adding hydraulic inductance L.sub.h and L.sub.p. Hydraulic inductance L.sub.h is obtained by summing various hydraulic inductances contributed by each segment of the combined pressure sensing orifice and passages according to the equation ##EQU4## where L.sub.nh is hydraulic inductance of the nth segment, l.sub.nh is length of the nth segment and A.sub.nh is cross-sectional area of the nth segment.
Resonant frequency can be found by ##EQU5## Typical values for the above parameters as found in production flow control sub-assemblies are in the order of ##EQU6## from which the resonant frequency is found to be about EQU f.sub.n =8 Hz.
Frequencies near this low resonant frequency are easily excited when such vehicles are subject to parking loads. The result can be resonance either at some sub-harmonic of the 36 Hz firing rate or the 12 Hz fundamental frequency itself. Thus, low frequency oscillations at frequencies such as 6 Hz, 9 Hz or 12 Hz are possible.
The flow non-linearities that can excite such oscillations include the following situations.
If the flow rate is too small to generate a pressure differential sufficient to cause the flow control piston to move against the pressure of the spring to a position where there is any opening of the bypass hole, then pump pressure supplementally increases to the point where the flow control piston is just lifted off the end of the output fitting. In this case, the flow resistance formed by the gap between the flow control piston and the end of the output fitting is just sufficient to support the supplemental pump pressure. If the pump flow is varying as described above, then this gap must vary as well and that initiates the oscillation. The oscillation then feeds upon itself and causes increased values of gap variation. This condition is further described below.
If the flow rate is just sufficient to activate the flow control piston-bypass hole interface and the flow is similarly varying, then the flow control piston is again driven into oscillation. In this case, the flow through the bypass hole has a significantly non-linear relationship with the pump variations and can even shut off during a cycle. This is quite sufficient to initiate a sub-harmonic oscillation of the above mentioned 36 Hz frequency signal. For a further discussion of stability problems in servo systems see DiStefano et al cited above.
The result can be unstable operation of the power steering system wherein it is subject to oscillations at these frequencies. Because the offending oscillation is due to an actual resonance, very significant perturbations of the open-loop gain and phase angle functions of the system result. The oscillations of the power steering system are the result of supplemental unity gain cross-overpoints in the open loop gain characteristic. It should be pointed out that these instabilities may very well be present in addition to others already present (i.e., such as shudder due to another unity gain crossover near 36 Hz). In any case, since any of these resonances result in significant flow and concomitant pressure variations being impressed directly across the power piston of the host steering gear, the phenomenon known as shudder occurs where a significant vibration is felt both in the vehicle structure and steering wheel.